@prefix owl:	<http://www.w3.org/2002/07/owl#> .
@prefix dbpedia-wikidata:	<http://wikidata.dbpedia.org/resource/> .
@prefix dbpedia-ja:	<http://ja.dbpedia.org/resource/> .
dbpedia-wikidata:Q3489869	owl:sameAs	dbpedia-ja:Sumset .
@prefix dbo:	<http://dbpedia.org/ontology/> .
dbpedia-ja:Sum-free_set	dbo:wikiPageWikiLink	dbpedia-ja:Sumset .
@prefix rdfs:	<http://www.w3.org/2000/01/rdf-schema#> .
dbpedia-ja:Sumset	rdfs:label	"Sumset"@ja ;
	rdfs:comment	"\u306B\u304A\u3044\u3066\u3001\u52A0\u6CD5\u7FA4 G \u306E 2\u3064\u306E\u90E8\u5206\u96C6\u5408 A \u3068 B \u306E\u548C\uFF08\u308F\u3001\u82F1: sum\uFF09\u3068\u306F\u3001A \u3068 B \u306E\u5143\u3054\u3068\u306E\u548C\u5168\u4F53\u306E\u6210\u3059\u96C6\u5408 \u3092\u8A00\u3046\u3002\u540C\u3058\u3082\u306E\u3092\u3001\u30A2\u30D5\u30A3\u30F3\u5E7E\u4F55\u5B66\u5468\u8FBA\u5206\u91CE\u3067\u306F (Minkowski sum) \u3068\u3082\u547C\u3076\u3002\u4F8B\u3048\u3070\u7DDA\u578B\u4EE3\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u4E8C\u3064\u306E\u7DDA\u578B\u90E8\u5206\u7A7A\u9593 U, V \u306E(sum space) U + V \u306F\u3053\u306E\u610F\u5473\u306E\u548C\u96C6\u5408\u3068\u3057\u3066\u5B9A\u7FA9\u3055\u308C\u308B\u3002 A \u306E n-\u91CD\u53CD\u5FA9\u548C\u96C6\u5408 (n-fold iterated sumset)\uFF08n-\u500D\u96C6\u5408\uFF09\u3068\u306F \u306E\u3053\u3068\u3068\u3059\u308B\uFF08\u3053\u3053\u3067\u3001n \u306F\u53F3\u8FBA\u306E\u9805\u6570\u3067\u3042\u308B\uFF09\u3002 \u52A0\u6CD5\u7684\u7D44\u5408\u305B\u8AD6\u3084\u306E\u591A\u304F\u306E\u554F\u984C\u3084\u7D50\u679C\u3092\u3001\u3053\u306E\u548C\u96C6\u5408\u3092\u7528\u3044\u3066\u8A00\u3044\u8868\u3059\u3053\u3068\u304C\u3067\u304D\u308B\u3002\u4F8B\u3048\u3070\u3001\u30E9\u30B0\u30E9\u30F3\u30B8\u30E5\u306E\u56DB\u5E73\u65B9\u5B9A\u7406\u306F\u6B21\u306E\u5F62\u3067\u8868\u3059\u3053\u3068\u304C\u3067\u304D\u308B\u3002 \u3053\u3053\u306B\u3001 \u306F\u5E73\u65B9\u6570\u5168\u4F53\u306E\u6210\u3059\u306E\u96C6\u5408\u3001N \u306F\u81EA\u7136\u6570\u5168\u4F53\u306E\u6210\u3059\u96C6\u5408\u3067\u3042\u308B\u3002\u591A\u304F\u306E\u7814\u7A76\u304C\u306A\u3055\u308C\u308B\u4E3B\u984C\u3068\u3057\u3066\u3001\"small doubling\"\uFF08\u5C0F\u3055\u3044\u500D\u5316\uFF09\u3092\u6301\u3064\u96C6\u5408\uFF08\u3059\u306A\u308F\u3061\u30012-\u500D\u96C6\u5408 A + A \u306E\u5927\u304D\u3055\u304C\uFF08A \u306B\u6BD4\u3079\u3066\uFF09\u5C0F\u3055\u304F\u306A\u308B\u3088\u3046\u306A\u96C6\u5408 A\uFF09\u306E\u554F\u984C\u304C\u3042\u308B\u3002(Freiman's theorem)\u306E\u4F8B\u3092\u53C2\u7167\u3002"@ja ;
	owl:sameAs	<http://rdf.freebase.com/ns/m.03pm7q> .
@prefix dct:	<http://purl.org/dc/terms/> .
dbpedia-ja:Sumset	dct:subject	<http://ja.dbpedia.org/resource/Category:\u7D44\u5408\u305B\u8AD6> ,
		<http://ja.dbpedia.org/resource/Category:\u6570\u5B66\u306B\u95A2\u3059\u308B\u8A18\u4E8B> ,
		<http://ja.dbpedia.org/resource/Category:\u52A0\u6CD5\u7684\u6574\u6570\u8AD6> ;
	dbo:wikiPageID	2933783 ;
	dbo:wikiPageRevisionID	81140291 ;
	dbo:wikiPageWikiLink	dbpedia-ja:Sum-free_set ,
		<http://ja.dbpedia.org/resource/\u81EA\u7136\u6570> ,
		<http://ja.dbpedia.org/resource/\u30A2\u30D5\u30A3\u30F3\u5E7E\u4F55\u5B66> ,
		<http://ja.dbpedia.org/resource/\u7DDA\u578B\u90E8\u5206\u7A7A\u9593> ,
		<http://ja.dbpedia.org/resource/Category:\u52A0\u6CD5\u7684\u6574\u6570\u8AD6> ,
		<http://ja.dbpedia.org/resource/Category:\u7D44\u5408\u305B\u8AD6> ,
		<http://ja.dbpedia.org/resource/\u7DDA\u578B\u4EE3\u6570\u5B66> ,
		<http://ja.dbpedia.org/resource/Category:\u6570\u5B66\u306B\u95A2\u3059\u308B\u8A18\u4E8B> ,
		<http://ja.dbpedia.org/resource/\u30A2\u30FC\u30D9\u30EB\u7FA4> ,
		dbpedia-ja:Graduate_Texts_in_Mathematics ,
		<http://ja.dbpedia.org/resource/\u5E73\u65B9\u6570> ,
		<http://ja.dbpedia.org/resource/\u56DB\u5E73\u65B9\u5B9A\u7406> ,
		<http://ja.dbpedia.org/resource/\u30B7\u30E5\u30CB\u30EC\u30EB\u30DE\u30F3\u5BC6\u5EA6> ,
		<http://ja.dbpedia.org/resource/\u6FC3\u5EA6_(\u6570\u5B66)> ,
		dbpedia-ja:Springer-Verlag ;
	dbo:wikiPageExternalLink	<http://www.krieger-publishing.com/subcats/MathematicsandStatistics/mathematicsandstatistics.html> .
@prefix prop-en:	<http://ja.dbpedia.org/property/> .
@prefix template-en:	<http://ja.dbpedia.org/resource/Template:> .
dbpedia-ja:Sumset	prop-en:wikiPageUsesTemplate	template-en:Math ,
		template-en:Lang-en-short ,
		template-en:Cite_book ,
		template-en:Planetmath_reference ,
		template-en:Mvar ,
		template-en:MathWorld ,
		<http://ja.dbpedia.org/resource/Template:\u4EEE\u30EA\u30F3\u30AF> ,
		template-en:Otheruses ;
	prop-en:author	"Noe, Tony."@ja ;
	prop-en:id	7060 ,
		3830 ;
	prop-en:title	"Minkowski sum"@ja ,
		"Sumset"@ja ,
		"sumset"@ja ,
		"Minkowski Sum"@ja ;
	prop-en:urlname	"Sumset"@ja ,
		"MinkowskiSum"@ja ;
	dbo:abstract	"\u306B\u304A\u3044\u3066\u3001\u52A0\u6CD5\u7FA4 G \u306E 2\u3064\u306E\u90E8\u5206\u96C6\u5408 A \u3068 B \u306E\u548C\uFF08\u308F\u3001\u82F1: sum\uFF09\u3068\u306F\u3001A \u3068 B \u306E\u5143\u3054\u3068\u306E\u548C\u5168\u4F53\u306E\u6210\u3059\u96C6\u5408 \u3092\u8A00\u3046\u3002\u540C\u3058\u3082\u306E\u3092\u3001\u30A2\u30D5\u30A3\u30F3\u5E7E\u4F55\u5B66\u5468\u8FBA\u5206\u91CE\u3067\u306F (Minkowski sum) \u3068\u3082\u547C\u3076\u3002\u4F8B\u3048\u3070\u7DDA\u578B\u4EE3\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u4E8C\u3064\u306E\u7DDA\u578B\u90E8\u5206\u7A7A\u9593 U, V \u306E(sum space) U + V \u306F\u3053\u306E\u610F\u5473\u306E\u548C\u96C6\u5408\u3068\u3057\u3066\u5B9A\u7FA9\u3055\u308C\u308B\u3002 A \u306E n-\u91CD\u53CD\u5FA9\u548C\u96C6\u5408 (n-fold iterated sumset)\uFF08n-\u500D\u96C6\u5408\uFF09\u3068\u306F \u306E\u3053\u3068\u3068\u3059\u308B\uFF08\u3053\u3053\u3067\u3001n \u306F\u53F3\u8FBA\u306E\u9805\u6570\u3067\u3042\u308B\uFF09\u3002 \u52A0\u6CD5\u7684\u7D44\u5408\u305B\u8AD6\u3084\u306E\u591A\u304F\u306E\u554F\u984C\u3084\u7D50\u679C\u3092\u3001\u3053\u306E\u548C\u96C6\u5408\u3092\u7528\u3044\u3066\u8A00\u3044\u8868\u3059\u3053\u3068\u304C\u3067\u304D\u308B\u3002\u4F8B\u3048\u3070\u3001\u30E9\u30B0\u30E9\u30F3\u30B8\u30E5\u306E\u56DB\u5E73\u65B9\u5B9A\u7406\u306F\u6B21\u306E\u5F62\u3067\u8868\u3059\u3053\u3068\u304C\u3067\u304D\u308B\u3002 \u3053\u3053\u306B\u3001 \u306F\u5E73\u65B9\u6570\u5168\u4F53\u306E\u6210\u3059\u306E\u96C6\u5408\u3001N \u306F\u81EA\u7136\u6570\u5168\u4F53\u306E\u6210\u3059\u96C6\u5408\u3067\u3042\u308B\u3002\u591A\u304F\u306E\u7814\u7A76\u304C\u306A\u3055\u308C\u308B\u4E3B\u984C\u3068\u3057\u3066\u3001\"small doubling\"\uFF08\u5C0F\u3055\u3044\u500D\u5316\uFF09\u3092\u6301\u3064\u96C6\u5408\uFF08\u3059\u306A\u308F\u3061\u30012-\u500D\u96C6\u5408 A + A \u306E\u5927\u304D\u3055\u304C\uFF08A \u306B\u6BD4\u3079\u3066\uFF09\u5C0F\u3055\u304F\u306A\u308B\u3088\u3046\u306A\u96C6\u5408 A\uFF09\u306E\u554F\u984C\u304C\u3042\u308B\u3002(Freiman's theorem)\u306E\u4F8B\u3092\u53C2\u7167\u3002"@ja .
@prefix xsd:	<http://www.w3.org/2001/XMLSchema#> .
dbpedia-ja:Sumset	dbo:wikiPageLength	"3209"^^xsd:nonNegativeInteger .
@prefix prov:	<http://www.w3.org/ns/prov#> .
dbpedia-ja:Sumset	prov:wasDerivedFrom	<http://ja.wikipedia.org/wiki/Sumset?oldid=81140291&ns=0> .
@prefix foaf:	<http://xmlns.com/foaf/0.1/> .
@prefix ns11:	<http://ja.wikipedia.org/wiki/> .
dbpedia-ja:Sumset	foaf:isPrimaryTopicOf	ns11:Sumset .
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<http://ja.dbpedia.org/resource/\u51F8\u96C6\u5408>	dbo:wikiPageWikiLink	dbpedia-ja:Sumset .
ns11:Sumset	foaf:primaryTopic	dbpedia-ja:Sumset .
@prefix rdf:	<http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
<http://ja.dbpedia.org/data/Sumset.ntriples>	rdf:type	foaf:Document ;
	foaf:primaryTopic	dbpedia-ja:Sumset .